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New converses of Jensen inequality via Green functions with applications

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

The Jensen inequality has many applications in several fields such as mathematics, statistics and economics etc. There are a lot of results devoted to the Jensen inequality concerning refinements, generalizations and converses etc. The main aim of this paper is to use new idea and present converses of the Jensen inequality with the help of Green functions. By virtue of these results, we obtain converses of Hölder and Levinson’s inequalities. At the end we present several applications of these results in information theory. The idea used in this paper may stimulate further research for the Jensen inequality.

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Acknowledgements

This work was supported by the Natural Science Foundation of China (Grant nos. 61373169, 11701176, 11626101, 11601485), the Science and Technology Research Program of Zhejiang Educational Committee (Grant no. Y201635325). The authors would like to express their sincere thanks to the anonymous reviewers for their helpful comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, University of Peshawar, Peshawar, 25000, Pakistan

    Shahid Khan & Muhammad Adil Khan

  2. Department of Mathematics, Huzhou University, Huzhou, 313000, China

    Yu-Ming Chu

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  1. Shahid Khan
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  2. Muhammad Adil Khan
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  3. Yu-Ming Chu
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Correspondence to Yu-Ming Chu.

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Khan, S., Khan, M.A. & Chu, YM. New converses of Jensen inequality via Green functions with applications. RACSAM 114, 114 (2020). https://doi.org/10.1007/s13398-020-00843-1

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